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A154348 a(n) = 16*a(n-1) - 56*a(n-2) for n>1, with a(0)=0, a(1)=1. 1
1, 16, 200, 2304, 25664, 281600, 3068416, 33325056, 361369600, 3915710464, 42414669824, 459354931200, 4974457389056, 53867442077696, 583309459456000, 6316374594945024, 68396663789584384, 740629643316428800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Third binomial transform of A164609, fourth binomial transform of A164608, fifth binomial transform of A054490, sixth binomial transform of A164607, seventh binomial transform of A083100, eighth binomial transform of A164683.

lim_{n -> infinity} a(n)/a(n-1) = 8 + 2*sqrt(2) = 10.8284271247....

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..135

Index entries for linear recurrences with constant coefficients, signature (16,-56).

FORMULA

a(n) = 16*a(n-1) - 56*a(n-2) for n>1, with a(0)=0, a(1)=1. - Philippe Deléham, Jan 12 2009

a(n) = ( (8 + 2*sqrt(2))^n - (8 - 2*sqrt(2))^n )/(4*sqrt(2)).

G.f.: 1/(1 - 16*x + 56*x^2). - Klaus Brockhaus, Jan 12 2009; corrected Oct 08 2009

E.g.f.: (1/(2*sqrt(2)))*exp(8*x)*sinh(2*sqrt(2)*x). - G. C. Greubel, Sep 13 2016

MATHEMATICA

Join[{a=1, b=16}, Table[c=16*b-56*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)

LinearRecurrence[{16, -56}, {1, 16}, 30] (* Harvey P. Dale, Aug 31 2016 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((8+2*r)^n-(8-2*r)^n)/(4*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 12 2009

CROSSREFS

Cf. A002193 (decimal expansion of sqrt(2)), A164609, A164608, A054490, A164607, A083100, A164683.

Sequence in context: A226869 A257289 A125451 * A129333 A001810 A016165

Adjacent sequences:  A154345 A154346 A154347 * A154349 A154350 A154351

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009

EXTENSIONS

Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009

Edited by Klaus Brockhaus, Oct 08 2009

STATUS

approved

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)